Dear Karl,

You've communicated *your* kaleidoscope rather wonderfully. Thank you!

I shall look into it...

Best wishes,


-----Original Message-----
From: "Karl Javorszky" <>
Sent: ‎12/‎02/‎2018 14:36
To: "Mark Johnson" <>
Cc: "fis" <>
Subject: Re: [Fis] The unification of the theories of information based on 
thecateogry theory

Kaleidoscope, Wittgenstein
Dear Mark,
thank you for your two questions. 
1)      Kaleidoscope
The term “kaleidoscope” is used to signify a complex thing that gives different 
pictures. The toy appears to produce an unlimited number of different pictures 
to the casual user. In fact, there is a maximal number of different pictures 
that can be produced, although this may not be immediately evident to every 
The term kaleidoscope was used to draw your attention to the manifold pictures 
that natural numbers generate when – as a collection – reordered. The diversity 
of pictures is indeed truly impressive. One may naively assume that there is an 
endless number of variations that can appear. This is but a subjective 
impression. In fact, if we deal with a limited number of distinguishable 
objects – which we, for convenience’s sake, enumerate -, there can appear only 
a limited number of different arrangements among these. 
How to generate cycles of expressions of (a,b) is as follows:
a)       Maximal numbers of elements in the kaleidoscope
We know that the optimal size – for information transmission purposes – for a 
collection is 136 elements, of which around 66 carry significant symbols. 
Therefore, we know also that no more than about 15 describing dimensions can be 
utilised to exhaustively describe a collection of that many elements. 
(Collections with more than 140 elements cannot be described consistently at 
all.)  Please see:   
b)      Generating the sorted collection of arguments (a,b)
We generate (a,b) by setting up two loops: 
begin outer loop
 a:1,16;  /* why 16: see above */
write value a;
begin inner loop; 
b: a,16 ;
write value b;
end inner loop; 
end outer loop. /* This gives us a table with 136 rows and 2 columns */
Then we sort the collection two times, once on (a,b), once on (b,a). We note 
the sequential number of each of the elements in both of the sorting orders. 
These we use to generate the cycles we are interested in (which we later 
compare to other cycles, from other reorders, as we build a more advanced 
version of the kaleidoscope). We see in this example cycles that appear during 
reorders from <sequential position resulting from a sorting operation where 
first sorting argument: a, second sorting argument: b> into <sequential 
position resulting from a sorting operation where first sorting argument: b, 
second sorting argument: a>. This classical introductory example and deictic 
definition is published in 
Please use this basic version of the kaleidoscope. One can add columns.
2)      Wittgenstein
Sitting in a snowy place and the Winter Olympics taking place right now, let me 
offer you my view of what Wittgenstein did in a parable about ski racing.
Philosophers are skiing athletes. Wittgenstein is a mediocre skier but a gifted 
mechanic. He introduces the concept of ski lifts to the sporting society. The 
ski lifts are a great invention and further the practice of skiing immensely. 
His co-athletes tell him, full of rightful indignation, that inventing, 
describing and operating a ski lift is not a sporting achievement, and falls 
definitely not under the term “skiing”. His results as an athlete are Zero.  He 
should be ashamed to try to tout a ski lift as a result of skiing. 
Wittgenstein, full of remorse, recants, agrees that ski lifts have nothing to 
do with the sport of skiing, and later in his life makes some irrelevant 
efforts of excellence in the sport sensu stricto.
Offering this audience of FIS participants:
a) a kaleidoscope which is exactly defined and delivers breath-taking pictures, 
b) an epistemological tool which generates undisputable facts about how <when, 
where, what and how much> are interdependent; these facts are of a numeric 
nature and root in a kind of arithmetic, so much simple, that there is a button 
on the screen of Excel for average users, enabling them to execute the 
this suggestion is outside of the subjects the scientists in FIS are 
researching, like using a ski lift is outside of sport. 
Accounting is not science. Forensic accounting makes life easier if one likes 
precision and exactitude. If one is interested in how place, number, amount 
translate into each other, here is a tool to study the question. There is an 
accounting link connecting the concepts mentioned above. It is multi-faceted 
and needs familiarisation – just like a kaleidoscope. This kaleidoscope is made 
of numbers. Please risk the effort and take a look at it. If your accountant 
says: this is worth looking into, it is usually reasonable to actually dedicate 
some thought to the approach. 

2018-02-12 10:46 GMT+01:00 Mark Johnson <>:

Dear Karl,

Do you really mean this?:
"As we look into a kaleidoscope, the first step is to make sure that we all 
look at a kaleidoscope, and preferably the same one. The next task is to make 
sure that we all perceive the same picture. As the kaleidoscope produces 
natural numbers, this should be a challenge that one can be expected to match. 
Only after it has been agreed that we all observe the same patterns is it 
reasonable to start discussing how to name the facts of perception."

I don't object to "looking at a kaleidoscope", but looking at the *same* 
kaleidoscope? How could we know? How is a kaleidoscope communicated?

Early Wittgenstein belonged to a philosophical tradition which was consumed by 
the idea of categories. In the Tractatus he sees (I think rightly) that the 
problems of philosophy result from confusion in language - but his approach is 
to "clarify" the categories and logic of language - which doesn't work. His 
later work is I think characterised by the insight that categories result from 
processes of conversation in ordinary language.

In cybernetics, we would say that the process that maintains a distinction is a 
transduction. If "my kaleidescope" and "your kaleidescope" are distinctions you 
and I make, then they result from transduction processes in me and you. If I 
was to say my kaleidescope is the same as yours, would I not have to know that 
my transduction process works in the same way as yours? Of course, I could just 
*say* it's the same without worrying about the details!

Transduction is a complicated affair. Wittgenstein said (Philosophical 
Investigations?... not sure) that if you saw a person performing a mathematical 
operation, you couldn't know exactly how they were thinking or if it was the 
same as your own thinking. Two sets of transducers may produce the same result 
but be fundamentally different underneath. 

If I say that my kaleidescope is the same as your kaleidescope then I have 
created a new category of "the same kaleidescope". What's that but a new 
transduction? But is my "same" the same as your "same"...?

Best wishes,


On 10 February 2018 at 18:36, Karl Javorszky <> wrote:

Using the logical language to understand Nature
The discussion in this group refocuses on the meaning of the terms “symbol”, 
“signal”, “marker” and so forth. This is a very welcome development, because 
understanding the tools one uses is usually helpful when creating great works. 
There is sufficient professional literature on epistemology, logical languages 
and the development of philosophy into specific sub-philosophies. The following 
is just an unofficial opinion, maybe it helps. 
Wittgenstein has created a separate branch within philosophy by investigating 
the structure and the realm of true sentences. For this, he has been mocked and 
ridiculed by his colleagues. Adorno, e.g. said that Wittgenstein had 
misunderstood the job of a philosopher: to chisel away on the border that 
separates that what can be explained and that what is opaque; not to elaborate 
about how one can express truths that are anyway self-evident and cannot be 
The Wittgenstein set of logical sentences are the rational explanation of the 
world. That, which we can communicate about, we only can communicate about, 
because both the words and what they mean are self-referencing. It is true that 
nothing ever new, hair-raising or surprising can come out of a logical 
discussion modi Wittgenstein, because every participant can only point out 
truths that are factually true, and these have always been true. There is no 
opportunity for discovery in rational thinking, only for an unveiling of that 
what could have been previously known: like an archaeologist can not be 

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